The three vertices of an equilateral triangle are represented by three complex numbers `z_1, z_2, z_3`. Then show that --
i) `\frac{1}{z_1 - z_2} + \frac{1}{z_2 - z_3} + \frac{1}{z_3 - z_1} = 0`
ii) `z_1^2 + z_2^2 + z_3^2 = z_1z_2 + z_2z_3 + z_3z_1`